Remark 6.3 
Everything said above is explicit.
In fact the generator set \(B_i\)  of \(PSL_2(q^i)\)  are given explicitly in [1]}.
Assume \(i\)  is even.
Let \(\textbf {i} \in \mathbb {F}_{q^i}\)  be such that \(\textbf {i} \notin \mathbb {F}_q\)  and \(\varepsilon = \textbf {i}^2 + \textbf {i} \in \mathbb {F}_q\) .
Let \(x\in \mathbb {F}_{q^i}\)  be such that \(1,x,\ldots ,x^{e_i-1}\)  form a basis for \(\mathbb {F}_{q^i}\)  over \(\mathbb {F}_q\) .
Then the \(q+1\)  elements of \(B_i\)  are
\( \phi _{i}(b_j)=\left(\begin{array}{cc} 1 & \gamma _j + \delta _j\textbf {i}\\ x(\gamma _j + \delta _j + \delta _j\textbf {i}) & 1 \end{array}\right),\qquad j=0,\ldots ,q,\) 
